2019/07/12 by Pier Paolo La Pastina, La Pastina, Pier Paolo, Luca Vitagliano +1
Mathematics · Medicine · #Homotopy and Cohomology in Algebraic Topology #Advanced Topics in Algebra #Ophthalmology and Eye Disorders
paper · pdf · doi:10.48550/arxiv.1907.05670
VB-groupoids are vector bundles in the category of Lie groupoids. They encompass several classical objects, including Lie group representations and 2-vector spaces. Moreover, they provide geometric pictures for 2-term representations up to homotopy of Lie groupoids. We attach to every VB-groupoid a cochain complex controlling its deformations and discuss its fundamental features, such as Morita invariance and a van Est theorem. Several examples and applications are given.